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Ruin probability in heavy tailed risk models

Year 2011, Volume: 4 Issue: 2, 39 - 56, 23.07.2011

Abstract

In this study, detailed information about heavy tailed distributions and the )ts sub-classes are revieved and the

conditions necessary for any distribution to belonging to one of these special classes of distributions are

explained. It is showed that how the ruin probabilities of a risk process that includes heavy tailed claim severity

amounts, can be calculated with theoretical justifications. An application is provided by using compulsory

traffic insurance data in Turkey in Matlab programming language. It is investigated if the loss severities can be

categorized under the heavy-tailed distribution and also the relevant sub-categorized of the distribution is

determined,too. Moreover, ruin probabilities are calculated in terms of different initial surplus and safety

factors by analyzing the risk process for this particular time.

References

  • [1] Asmussen, S., 2000, Ruin probabilities, Advanced Series on Statistical Science and Applied Probability Vol.2, World Scientific Publishing, Singapore, 385p.
  • [2] Bingham, N.H., Goldie, C.M., Teugels, J.L., 1987, Regular variation, Cambridge University Press, Cambridge.
  • [3] Chistyakov, V.P., 1964, A theorem on sums of independent positive random variables and its applications to branching random processes, Theory probability Application 9, pp 640-649.
  • [4] Embrechts, P., Goldie, C.M., 1982, On convolution tails, Stochastic Processes Applied 13, pp 263-278.
  • [5] Embrechts, P., Klüppelberg C., Mikosch T., 2001, Modelling Extremal Events for Insurance and Fnance, Applications of Mathematics Stochastic Modelling and Applied Probability 33 , Springer, 648p.
  • [6] Goldie, C. M., Klüppelberg C., 1998, Subexponential Distributions, A practical guide to heavy tails: statistical techniques and applications, pp 435-460.
  • [7] Klugman, S.,A., Panjer H.H., Willmot G.,E., 2008, Loss models from data to decisions, Third Edition, John Wiley and Sons, New Jersey, 726p.
  • [8] Klüppelberg, C., 1988, Subexponential distributions and integrated tails, Journal of Applied Probability,Vol 25,No:1,pp 132-14.1
  • [9] Mo, K.C.K., 2002, Ruin probabilities with dependent claims, Actuarial Studies, Faculty of Commerce and Economics, University of New South Wales, 50p.
  • [10] Rolski T., Schmidli H., Schmidt V., Teugels J., 1999, Stochastic processes for Insurance and Finance, Wiley Series in Probability and Statstics, John Wiley and Sons, England, 654p.
  • [11] Sigman K., 1999, Appendix: A primer on heavy-tailed distributions, Queueing Systems 33, pp 261-275

Kalın kuyruklı risk modellerinde iflas olasılığı

Year 2011, Volume: 4 Issue: 2, 39 - 56, 23.07.2011

Abstract

 Bu
çal
ışmada, hasar tutarlarının
kal
ın kuyruklu dağılım
yap
ısına
uyup uymad
ığı, bu dağlım
yap
ısının
ko
şulları incelenerek
araştırılmıştır. Kal
ın kuyruklu dağılım
 yapısına
sahip risklerin, risk süreci ve iflas olas
ılıkları
üzerindeki etkisi teorik ispatlar eşliğinde
ıklanmaya çalışılmıştır.
Matlab yaz
ılımında
geli
ştirilen program
sayesinde, Türkiye Trafik Sigortası veri
kümesi kullan
ılarak, hasar
büyüklüklerinin kal
ın kuyruklu dağılıma
uyup uymadığı sorgulanmış
, uyması halinde ise hangi
alt s
ınıfa
dahil oldu
ğu araştırılmıştır.
Ayr
ıca belirlenen dönem
için risk süreci incelemesi yap
ılarak,
çe
şitli sermaye miktarı
ve güvenlik yükleme faktörlerine bağlı  olarak iflas olasılıkları  hesaplanmıştır.

References

  • [1] Asmussen, S., 2000, Ruin probabilities, Advanced Series on Statistical Science and Applied Probability Vol.2, World Scientific Publishing, Singapore, 385p.
  • [2] Bingham, N.H., Goldie, C.M., Teugels, J.L., 1987, Regular variation, Cambridge University Press, Cambridge.
  • [3] Chistyakov, V.P., 1964, A theorem on sums of independent positive random variables and its applications to branching random processes, Theory probability Application 9, pp 640-649.
  • [4] Embrechts, P., Goldie, C.M., 1982, On convolution tails, Stochastic Processes Applied 13, pp 263-278.
  • [5] Embrechts, P., Klüppelberg C., Mikosch T., 2001, Modelling Extremal Events for Insurance and Fnance, Applications of Mathematics Stochastic Modelling and Applied Probability 33 , Springer, 648p.
  • [6] Goldie, C. M., Klüppelberg C., 1998, Subexponential Distributions, A practical guide to heavy tails: statistical techniques and applications, pp 435-460.
  • [7] Klugman, S.,A., Panjer H.H., Willmot G.,E., 2008, Loss models from data to decisions, Third Edition, John Wiley and Sons, New Jersey, 726p.
  • [8] Klüppelberg, C., 1988, Subexponential distributions and integrated tails, Journal of Applied Probability,Vol 25,No:1,pp 132-14.1
  • [9] Mo, K.C.K., 2002, Ruin probabilities with dependent claims, Actuarial Studies, Faculty of Commerce and Economics, University of New South Wales, 50p.
  • [10] Rolski T., Schmidli H., Schmidt V., Teugels J., 1999, Stochastic processes for Insurance and Finance, Wiley Series in Probability and Statstics, John Wiley and Sons, England, 654p.
  • [11] Sigman K., 1999, Appendix: A primer on heavy-tailed distributions, Queueing Systems 33, pp 261-275
There are 11 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Başak Bulut

Cenap Erdemir This is me

Publication Date July 23, 2011
Published in Issue Year 2011 Volume: 4 Issue: 2

Cite

IEEE B. Bulut and C. Erdemir, “Kalın kuyruklı risk modellerinde iflas olasılığı”, JSSA, vol. 4, no. 2, pp. 39–56, 2011.